# The relationship between space and time

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Is there a physical explanation for this relationship  that exists apart from the geometrical explanations?

I think Einstein was at first unhappy with this geometrical representation but (I think) he came to accept it.

I have heard  that c  is only coincidentally  the same speed as light and ,apparently  the nature of spacetime itself is more fundamentally important ,and presumably this nature requires c .

I have also  heard c described as a "conversion factor" between space and time.

So how does c convert space into time? Or is this just a conversion factor in the sense of a mathematical  conversion.?

Does any spatial measurement also require a measurement of time and vice versa? Would that be a correct and useful  description of the nature of spacetime ?

Would it be just as correct to describe spacetime as"distance-time"?

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I’m not sure what you mean by “the geometrical explanations”

Time and space are related because the speed of light is invariant - the same in any inertial reference frame

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9 minutes ago, swansont said:

I’m not sure what you mean by “the geometrical explanations”

Time and space are elated because the speed of light is invariant - the same in any inertial reference frame

Would not space and time still be related even if the speed of light was not invariant? Or would such a situation lead to space and time being absolute and "standalone" features of nature?(Would they be related in a different way ,perhaps?)

Sorry ,yes "geometrical explanations" seems loose. Perhaps  I meant "mathematical equations/explanations ". or "maybe "geometrical representations"

I am trying to get at whether there is a physical relationship between space and time   aside from the mathematical relationships (not claiming  to have mastered that side of it  or anything like it)

Does it make any sense to ask if there is a physical relationship between space and time or can we only ask what are the relationships between our measurements of space and time.?

(I feel the second option may be the correct one and  all we can talk about  about is measurements.)

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Neither space nor time is a substance

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Space being just a volume has units of length. X,Y,Z by defining the invariant of c we can give time a unit of length as well by using the interval ct.

This gives 4 coordinates ct,x,y,z.

These are properties of spacetime.

The above describes the relationship between space and time. The x coordinate  and the ct interval vary with length contraction and time dilation. While c remains constant.

Edited by Mordred
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1 hour ago, Mordred said:

Space being just a volume has units of length. X,Y,Z by defining the invariant of c we can give time a unit of length as well by using the interval ct.

This gives 4 coordinates ct,x,y,z.

These are properties of spacetime.

The above describes the relationship between space and time. The x coordinate  and the ct interval vary with length contraction and time dilation. While c remains constant.

Is space as volume a thing?

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Volume is a property so is space. You can have a space devoid of all particles both virtual and real and still have space. This state is the Einstein vacuum. Under QM with the HUP zero point energy it's never obtainable but that doesn't change how space is defined.

Trying to think of space or spacetime as a thing,  substance, fabric , eather etc will always lead down the wrong garden path.

The term physical by definition " anything described by physics " makes volume a physical property by that definition. The term thing has no real meaning in physics.

Edited by Mordred
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4 minutes ago, Mordred said:

Volume is a property so is space. You can have a space devoid of all particles both virtual and real and still have space. This state is the Einstein vacuum. Under QM with the HUP zero point energy it's never obtainable but that doesn't change how space is defined.

Trying to think of space or spacetime as a thing,  substance, fabric , eather etc will always lead down the wrong garden path.

The term physical by definition " anything described by physics " makes volume a physical property by that definition. The term thing has no real meaning in physics.

Thanks Mordred, I'd not heard of the Einstein Vacuum before now. Up to you said that, I thought space could not be discrete unto itself, in principle. I know what you mean by not calling it a 'thing'.

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The Einstein vacuum is one of the classes of solutions of the Einstein field equation.  There are typically 3 primary classes of solutions in textbooks such as Introductory to General Relativity by Lewis Ryder for example.

The common solutions to the EFE taught from these textbooks at the Introductory level are typically

Einstein vacuum

Weak Newton approximation (planet's stars etc )

Schwartzchild metric blackholes.

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Thought c related to them being orthogonal.

Would see them swap in BH's.

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4 hours ago, Endy0816 said:

Thought c related to them being orthogonal.

Would see them swap in BH's.

?

Them?

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1 hour ago, swansont said:

?

Them?

Space and Time

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7 hours ago, Endy0816 said:

Thought c related to them being orthogonal.

Orthogonal refers to when two vectors are 90 degree perpendicular to one another. Coordinates can be regarded as vectors so the x axis is orthogonal to the y axis. In Cartesian coordinates with no time dilation the ct,x,y,z axis are orthogonal.

A little math trick anytime you see a tensor with only the diagonal components non zero the tensor is orthogonal

Here is the Minkowskii tensor as an example

$\eta_{\mu\nu}=\begin{pmatrix}-c^2&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}$


Edited by Mordred
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3 hours ago, Endy0816 said:

Space and Time

I don't think that makes much sense...spacetime is one entity, not two.

It maybe worth familiarising with the workings of light cones and see how they behave as they go past an event horizon.

If you were travelling into a black hole and you went past the EH, before the inevitable spaghettification you would not experience anything wacky (from your frame of reference).

However, what truly happens past the event horizon, regardless of what GR predicts and a number of other theories, still remains speculative.

Quote

Time and space are elated because the speed of light is invariant

Awww, that's so cute. Let's hope c stays invariant so time and space doesn't get all grumpy.

Edited by Royston
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The relationship between time and space is obvious, as they can be interchanged depending on one's frame of reference. The following couple of links may explain better then I ever could.....

https://einstein.stanford.edu/content/relativity/a10743.html
What is the relationship between space and time?
Mathematically, and in accordance with relativity, they are in some sense interchangeable, but we do know that they form co-equal parts of a larger 'thing' called space-time, and it is only within space-time that the most complete understanding of the motion and properties of natural objects and phenomena can be rigorously understood by physicists. Space and time are to space-time what arms and legs are to humans. In some sense they are interchangeable, but you cannot understand 10,000 years of human history without including both arms and legs as part of the basic human condition.

:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

https://www.physicsoftheuniverse.com/topics_relativity_spacetime.html

Another corollary of Special Relativity is is that, in effect, one person’s interval of space is another person’s interval of both time and space, and one person’s interval of time is also another person’s interval of both space and time. Thus, space and time are effectively interchangeable, and fundamentally the same thing (or at least two different sides of the same coin), an effect which becomes much more noticeable at relativistic speeds approaching the speed of light.

Einstein's former mathematics professor, Hermann Minkowski, was perhaps the first to note this effect (and perhaps understood it even better than Einsteinhimself), and it was he who coined the phrase “space-time” to describe the interchangeability of the four dimensions. In 1908, Minkowski offered a useful analogy to help explain how four-dimensionalspace-time can appear differently to two observers in our normal three-dimensional space. He described two observers viewing a three-dimensional object from different angles, and noting that, for example, the length and width can appear different from the different viewpoints, due to what we call perspective, even though the object is clearly one and the same in three dimensions.

The idea perhaps becomes even clearer when we consider that our picture of the Moon is actually what the Moon was like 1¼ seconds ago (the time light takes to reach the Earth from the Moon), our picture of the Sun is actually how it looked 8½ minutes ago, and by the time we see an image of Alpha Centauri, our nearest star system, it is already 4.3 years out of date. We can therefore never know what the universe is like at this very instant, and the universe is clearly not a thing that extends just in space, but in space-time

Due to the relativistic effects of previous section can be considered an example of this: whereas the stay-at-home twin’s progress through space-time was wholly through time, the traveling twin’s progress was partly through space, so that his progress through time was less than that of the stay-at-home twin (so that he aged less).

Therefore, as Einstein remarked, “For us physicists, the distinction between past, present and future is only an illusion, however persistent”, and these concepts really do not figure at all in Einstein’s justifiably famous formula, E = mc2, which we will look at in the next section.

Edited by beecee
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On 7/27/2019 at 12:54 PM, geordief said:

I think Einstein was at first unhappy with this geometrical representation but (I think) he came to accept it.

'Unhappy' might not be the right word. 'Superfluous' might be a better description of how Einstein reacted first on Minkowksi's mathematical 'games', of no importance. In the end, Minkowski was 'just' a mathematician, not a physicist, at least formally.

Later, Einstein discovered how important Minkowski's formalism was, and became in fact a very central point for general relativity.

Oh, and to add, the relationship between Minkowski and Einstein made a bad start. Minkowski was a mathematical teacher of Einstein at the Zürich Polytechnikum, and Minkowski described his student Einstein as a 'lazy bastard' (or something like that. At least the word 'lazy' is important...). Maybe that explains part of Einstein's disdain for Minkowski's games.

Edited by Eise
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5 minutes ago, Eise said:

'Unhappy' might not be the right word. 'Superfluous' might be a better description of how Einstein reacted first on Minkowksi's mathematical 'games', of no importance. In the end, Minkowski was 'just' a mathematician, not a physicist, at least formally.

Later, Einstein discovered how important Minkowski's formalism was, and became in fact a very central point for general relativity.

Oh, and to add, the relationship between Minkowski and Einstein made a bad start. Minkowski was a mathematical teacher of Einstein at the Zürich Polytechnikum, and Minkowski described his student Einstein as a 'lazy bastard' (or something like that. At least the word 'lazy' is important...). Maybe that explains part of Einstein's disdain for Minkowski's games.

Thanks,that is interesting.Funny too on the face of it.

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• 4 weeks later...
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# The relationship between space and time

Many have wrestled with this question over the centuries

But in asking it you are pulling in some of the territory of Philosophy.

So you have said The relationship...

That begs the first question if there is a relationship is it unique  or are there more than one?

You seem to expect there to be multiple relationships since you have said;

On 7/27/2019 at 11:54 AM, geordief said:

Is there a physical explanation for this relationship  that exists apart from the geometrical explanations?

Then again others have noted that

On 7/27/2019 at 10:01 PM, Mordred said:

Volume is a property so is space. You can have a space devoid of all particles both virtual and real and still have space. This state is the Einstein vacuum. Under QM with the HUP zero point energy it's never obtainable but that doesn't change how space is defined.

Trying to think of space or spacetime as a thing,  substance, fabric , eather etc will always lead down the wrong garden path.

The term physical by definition " anything described by physics " makes volume a physical property by that definition. The term thing has no real meaning in physics.

Declaring at least space to be a property.
That clearly begs the question

Property of what?
Can a property posses a property?

Which merely pushes the question further back up the line.

Again exploring the geometrical and trying to link it to other physical notions we have

On 7/29/2019 at 10:23 AM, Eise said:

Later, Einstein discovered how important Minkowski's formalism was, and became in fact a very central point for general relativity.

I would suggest that one important link between space and time, whatever their nature, is motion.

But saying 'motion' is just a wooly word by itself and also begs the question

Motion of what?

Which introduces both the need for (mathematical) formalism and some 'object' or 'objects' to which we can attribute 'properties'.

Given the mathematical formalism of a frame of reference we can introduce properties such as position and orientation along with temporal property
of elapsed time.
Combining these leads to motion, both translational and rotational.

These objects may also have other properties (such as temperature) that are unrelated to space or time.

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Recently visited my aunt in Zurich, prior to my Italian vacation, and went into a little café by the Zurich Polytechnic.
I was told that this café was frequented by A Einstein during breaks.

I forget the name of the café, but maybe Eise can confirm ?

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34 minutes ago, studiot said:

I would suggest that one important link between space and time, whatever their nature, is motion.

But saying 'motion' is just a wooly word by itself and also begs the question

Motion of what?

Which introduces both the need for (mathematical) formalism and some 'object' or 'objects' to which we can attribute 'properties'.

Given the mathematical formalism of a frame of reference we can introduce properties such as position and orientation along with temporal property
of elapsed time.
Combining these leads to motion, both translational and rotational.

These objects may also have other properties (such as temperature) that are unrelated to space or time.

What might be the state of motion within a black hole? Are all objects there identical? Is there no separation between any objects? Just one object? Any gravitons?

Is it essential to have a decent  understanding of what happens there before we can hope to start to talk about anything fundamental in the world we can observe?

All I have heard is that only (pure) spacetime exists there (which makes little sense to me)

56 minutes ago, MigL said:

Recently visited my aunt in Zurich, prior to my Italian vacation, and went into a little café by the Zurich Polytechnic.
I was told that this café was frequented by A Einstein during breaks.

I forget the name of the café, but maybe Eise can confirm ?

Maybe some of his genius rubbed off?

They might run a tourist line in Aladdin like souvenir  trinkets.

1 hour ago, studiot said:

So you have said The relationship...

That begs the first question if there is a relationship is it unique  or are there more than one?

You seem to expect there to be multiple relationships since you have said;

I had in mind the relationship we are trying  to model.It reminds me of the philosophical idea where it was once believed that "redness" was an actual thing that red things so to speak dipped their nibs in(forget what school of philosophy that was,maybe Aristotle?)

Anyway ,the relationship may not be a physical thing but we treat it as if it was .Like a mirage in the desert ,the better we understand it the further away it gets....

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47 minutes ago, geordief said:

What might be the state of motion within a black hole? Are all objects there identical? Is there no separation between any objects? Just one object? Any gravitons?

Is it essential to have a decent  understanding of what happens there before we can hope to start to talk about anything fundamental in the world we can observe?

All I have heard is that only (pure) spacetime exists there (which makes little sense to me)

I had in mind the relationship we are trying  to model.It reminds me of the philosophical idea where it was once believed that "redness" was an actual thing that red things so to speak dipped their nibs in(forget what school of philosophy that was,maybe Aristotle?)

Anyway ,the relationship may not be a physical thing but we treat it as if it was .Like a mirage in the desert ,the better we understand it the further away it gets....

"What might be the state of motion within a black hole?"

Once again I council fully grasping a simple model before trying to tackle the most difficult ones that even our best scientists have yet to grasp.

In posting in this thread I am trying to continue the foundation I posted in your other thread on this subject.

Here is a simple example.

Take Newton's second law.

$F = ma = m\frac{{dv}}{{dt}} = m\frac{{{d^2}x}}{{d{t^2}}} = m\frac{d}{{dt}}\left( {\frac{{dx}}{{dt}}} \right)$

Where F is the force applied, to mass m, x is a one dimensional coordinate in frame X1 and v is the velocity.

This can be solved to give a simple equation without the calculus derivatives, especially if F is set equal to  0.

Edited by studiot
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20 hours ago, MigL said:

I forget the name of the café, but maybe Eise can confirm ?

No, sorry. It is true that Zürich is only 30 kilometers away, but it is already years ago that I was there. I have no details. I would have to google, just like you.

But of course, even if Bern is much farther away, I was already 2 times at my 'favourite pilgrimage place': the Einstein house. That was the place where he lived in his famous year 1905, where he explained the brownian movement, wrote his article about special relativity, and on the existence of what later would be called photons.I am a rationalist.But sometimes a romanticist too...

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On 8/26/2019 at 3:49 PM, studiot said:

Here is a simple example.

Take Newton's second law.

F=ma=mdvdt=md2xdt2=mddt(dxdt)

Where F is the force applied, to mass m, x is a one dimensional coordinate in frame X1 and v is the velocity.

This can be solved to give a simple equation without the calculus derivatives, especially if F is set equal to  0.

Should I set the observer at the CoG point?(where the sum of F's =0)

So there x=0 and  the acceleration  times the mass  of the object with mass m1 and the acceleration times the mass of the object with mass mare equal and opposite.

Which leads to the accelerations of the two objects being inversely proportional to their respective masses.

a sub1/a sub2  =m subscr2/m subscr1

Is that it?

Edited by geordief
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11 hours ago, geordief said:

Should I set the observer at the CoG point?(where the sum of F's =0)

So there x=0 and  the acceleration  times the mass  of the object with mass m1 and the acceleration times the mass of the object with mass mare equal and opposite.

Which leads to the accelerations of the two objects being inversely proportional to their respective masses.

a sub1/a sub2  =m subscr2/m subscr1

Is that it?

Yes this is good stuff, but we need to do more.

Since it is going to be raining all afternoon I will take the opportunity to expand on my equations.

Whilst you are waiting I suggest you consider the idea that Force is a function of position, x. (rather than comparing two accelerations)

So what happens if we choose different one-dimensional frames?

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5 hours ago, studiot said:

Yes this is good stuff, but we need to do more.

Since it is going to be raining all afternoon I will take the opportunity to expand on my equations.

Whilst you are waiting I suggest you consider the idea that Force is a function of position, x. (rather than comparing two accelerations)

So what happens if we choose different one-dimensional frames?

I can think of the frame of msub1  ,the frame of msub2  and the frame of any x.

Is that where I should be thinking about?

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